To compare the \(A_\alpha \) -spectral radii of mixed graphs, we first introduced a useful tool called the Kelmans transformation. The Kelmans transformation,
of an undirected graph, or called graph compression, was defined by A.K. Kelmans in 1981[1]}. The authors Kao and Weng have generalized it into a matrix version in [2]}, and here we will further generalize the transformation to fit the \(A_\alpha \)  matrix.
